Implementation of the ideal algorithm on unsteady two-phase flows and application examples

For unsteady two-phase flows, the most widely used numerical approaches for coupled solution of continuity and momentum equations are fractional-step methods and SIMPLE-family algorithms. Fractional-step methods have advantages in their fast convergence rates, while their disadvantages lie in conditional stability for initial-value problems. SIMPLE-family algorithms are absolutely stable; however, their convergence rates are slow. To overcome the shortcoming of traditional SIMPLE-family algorithms the, IDEAL algorithm is proposed by the present authors. It is concluded that the IDEAL algorithm overcomes the shortcoming of traditional SIMPLE-family algorithms, thus possessing two advantages of fast convergence rate and absolute stability simultaneously.